I am so sorry to hear your news about your grandmother. What an unhappy shock this must be for you right now, and I can really hear how frightened you are by all of this.
It is okay to feel frightened. It is ok to cry and to be upset about what is happening. These are "Big" things, and they are never easy for anyone to face.
You are worried about how to deal with all of this right now. That is not surprising. When your grandfather died you didn't want to feel the pain of his loss, and that too is so normal! Many people 'deaden' their emotions after a loss like that. You're right, it is so much easier to deal with pain if you don't have to feel it right away. The human spirit is very resiliant, though. As you begin to recover from the shock of losing your loved one, you begin to feel a little bit more and more each day until one day the sadness will come back but it won't be that horrible big sadness that you can't deal with. It will be just big enough that you will cry and mourn and deal with it all. Then you can start to heal. It can take 2 years or more for that to happen. It sounds like when your grandfather passed away you were quite young, and that is even more overwhelming.
I do see two good things in your news that I would like to share with you. One, I have to chuckle that your Grandmother, who should be eating her meals herself, still 'sneaks' food to her dogs. That is so cute:-). They obviously mean a lot to her and this is one way she has of showing them that she loves them. I am sure she feels very empowered when she is able to give her meals to the dogs - kind of like a way of being rebellious when everyone is trying to take control away from her. She is saying, I am still in control:-). I wouldn't chide her on that. Maybe you can even become a co-conspirator with her and both of you can 'sneak' food to the dogs. You may find her more willing to eat along with you that way.:-)
The other good thing is that you have learned that you still have some time to spend with your grandmother. How much worse would it be to hear she had died without any warning, without a chance to get used to the knowledge, without a chance to say goodbye and without a chance to share with her the things you want her to know and that you want to know about her. I know it doesn't seem like a long time, but you will be surprised at how much you can do even in a short period of time.
One of the best gifts you can give to your grandmother right now is to share whatever time she has left with her. If her health is this poor, I am sure she is not feeling very good and is often quite tired. She is probably feeling worried too, and I suspect she may be more worried about you and the other family members than about herself. She is probably concerned about what will happen to her dogs. This is a time to listen to her. Ask her if there is anything you can do for her, like walking her dogs for her, or running errands, or things like that, to show you you care and you understand.
Being able to accept that someone you love is dying is a very difficult thing to do, but it is also a very powerful one. They are the one facing death. We are the ones facing their loss - and not only does it hurt, it can be scary. Sometimes facing the things we fear can give you whatever strength you need to deal with the situation.
Take this time to get to know your grandmother even better than you do - not just as your grandmother, but as the woman she was during her life. You have this opportunity, and you know you will have a little bit of time. She may be happy to have someone who wants to 'know' the real her and who can remember the person after she has gone.
It will still hurt like crazy when the time does come. Don't worry about facing her death right now because there will be time enough when it happens. Instead, take the time right now to face her 'living', and you may be surprised at how strong you will be when the time comes. Don't be afraid of your tears, either. They too are a gift that shows to you and to her and everyone else that you know what it feels like to love.
My heart and prayers are with you and your grandmother right now. Take care of yourself and remember, it is alright to feel so sad.